About Two Equation Turbulence Modelling?
 

Hello all.

I'm very curious how people develop epsilon equation and how the equation
can provide a length scale to calculate the turbulent viscosity?

And, for the low reynolds number two equation models why an ad hoc term is added to the equations?

Any quick answers or references recommended to help to understand the problems?

Thanks.

Eddy viscosity-based turbulence models, i.e. k-epsilon, were developed under certain assumptions. For instance the turbulent flow is assumed to be isotropic, large eddies at the order of flow domain possess all contents of the turbulent kinetic energy while dissipation of turbulent kinetic energy is only done in very small scales of the flow at the order of kolmogorov length scale. These simplifying assumptions together with serious experimental works can help the expert find order of magnitudes of different parameters and introduce their models.
However, In order to have better models, simplifying assumptions like ones described above should be revised. For example turbulent flow is not isotropic at near wall regions, which is not considered in standard two-equation models. In fact standard models can only give acceptable predictions in an isotropic high-Re flow far away from solid walls. Therefore one should use either wall functions or add some correction terms to these models to find a more realistic prediction of flow behavior at these regions.
On the other hand, not all contents of a turbulent flow belongs to domain order eddies and dissipation also occurs in flow scales quite larger than kolmogorov length scale. In fact turbulent flow is a spectrum of eddies with different scales. With this point of view newer methods are developed which gives better predictions at the expense of higher calculation costs.
regards